The paper introduces TRADES (TRAnsformer-based Denoising Diffusion Probabilistic Engine for LOB Simulations), a novel generative model for creating realistic and responsive Limit Order Book (LOB) market simulations. TRADES leverages a conditional diffusion process with a transformer architecture to generate order flows as multivariate time series, conditioned on past orders and LOB snapshots. This approach addresses limitations of prior GAN-based methods, such as mode collapse and training instability, and improves upon traditional agent-based simulations that oversimplify market dynamics. The model is trained in a self-supervised manner by adding noise only to the target future step and learning to denoise it, enabling autoregressive generation at inference time.

Key contributions include the first quantitative metric for market simulation evaluation—the predictive score, which measures the usefulness of synthetic data by training a price predictor on generated data and testing on real data. TRADES significantly outperforms state-of-the-art methods (CGAN and IABS) on Tesla and Intel stocks, achieving 3.27x and 3.48x improvements in predictive score. The generated simulations also exhibit high realism, covering 67% of the real data distribution in PCA space and reproducing important stylized facts such as volatility clustering and absence of return autocorrelation. Furthermore, TRADES demonstrates responsiveness to external agents in market impact experiments, enabling counterfactual analysis of trading strategies.

The authors release DeepMarket, an open-source Python framework for deep learning-based market simulation, along with TRADES-LOB, a synthetic LOB dataset. This work advances the field by providing a robust, quantitative evaluation framework and a practical tool for generating high-fidelity market data, with potential applications in strategy backtesting, market impact studies, and financial research.